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13Complex Systems of Charged Particles and their Interactions with Electromagnetic Radiation 2019
COMPLETE SEMI-PHENOMENOLOGICAL APPROACH TO PHOTOIONIZATION OF ENDOHEDRALS
12 2 M.Ya. Amusia ' , L. V. Chernysheva
1Racah Institute of Physics, the Hebrew University, Jerusalem, Israel e-mail: amusia@vms.huji.ac.il 2Ioffe Physical-Technical Institute of the Russian Academy of Sciences, St. Petersburg, Russian Federation, e-mail: Larissa.Chernyshevs@mail.ioffe.ru
We have calculated photoionization cross sections of endohedral atoms A@CN, for which developed an approach that is relatively simple and at the same time complete enough. For the first time, we took into account simultaneously the polarizability of the fullerene electron shell CN that modifies the incoming photon beam and the alteration of the one-electron wave functions of the caged atom A under the action of both CN and atom A polarization potentials. The properly modified one-electron wave functions became a starting point of the account of the multi-electron correlations in the frame of the random phase approximation with exchange (RPAE). As concrete objects, we have considered Ar and Xe atoms inside fullerene C60.
We demonstrate that the effect of polarizability of the fullerenes CN electron shell strongly affects the caged atom A photoionization cross section due to dynamic CN polarization, i.e. via the modification of the incoming photon beam that acts upon atom A, located inside CN, as a resonator or amplifier. To study this effect qualitatively, we assume the validity of a strong inequality rA ^ R, instead of a simple one rA < R (where rA and R are the atomic and CN radiuses, respectively) that took place in reality. In the lowest order in rA / R ^ 1 the effect of dynamic CN polarization is presented by photon frequency »dependent factor[1-aC(a)/2R3J, where aC(a) is the CN dynamic polarizability.
Along with this, we took into account the action of static polarization of CN. To do this, we used the following expression of the polarization potential UC of fullerene CN via its static dipole polarizability aC = aC (0): WC = -aC / 2(r2 + R2 )2 for r > R and WC = -aC / 8R4 for r < R. Along with CN polarization, we took into account in a similar approximation the polarization potential of the atom A itself by introducing the atomic polarization potential WA = -aA / 2(r2 + rA2 )2, where aA is the static atomic dipole polarizability.
In the calculations performed we describe the fullerenes shell by a Lorentz-shape potential UC (r) = -UoRd / [(r - R)2 + d2 J, where d is the potential width, while U0d / R is its depth. This
potential represents the charge density distribution in CN qualitatively better than the square well potentialpreviously used by us and most of researchers. Namely, the Lorentz-shape guaranties the three-layer charge distribution, with signs - + -, respectively, where + represents the smeared over fullerene surface carbon nuclear charges. The square well leads, instead, to the sequence (-+ +-), where (- +) and ( + -) layers separate the width of the potential UC.
The results obtained demonstrate profound influence of static and dynamic polarizabilities at low photon energies. Close to the ionization threshold the cross-section in Ar@C60 as compared to pure Ar increases by a factor more than 15. For the near threshold frequency region of Xe@C60 the same ratio reaches more than 20. Obviously, the influence of the fullerene shell dies out, as it should be, with the photon energy growth. For more details and concrete numerical results see [1].
References
[1] M. Ya. Amusia et al. 2019 JETP Letters109 (6)355.
